I don't entirely understand the question here. The Roman senate had no power to decide domestic, military, or foreign policy. It didn't have power to decide anything, actually--it was a purely advisory body, albeit an extremely influential one. All decisions were made by magistrates who were elected by various means. In military affairs the magistrates holding imperium held total power over their actions, and although the senate might send advice or protest the magistrate technically didn't have to listen to them (although if he didn't he'd have to answer for it after his term ended). And in Athens the Assembly didn't really decide military matters either. The ten strategoi, elected from each of the demes, conferred with each other and decided what to do with their respective commands and with each other. The Assembly could issue orders to the strategoi which were supposed to be followed, but these were generally broad things, such as the decision to massacre the Mytileneans (and the subsequent decision not to). But if we take a peek at the Peloponnesian War almost everything was decided by the strategoi in field commands. Demosthenes actually feared returning to Athens after the failure of his Aetolian campaign lest he be prosecuted for mismanagement of his command and stayed another year in the field, taking the time to start his startlingly successful Acarnanian campaign of his own initiative. Even a campaign like the proposed Boeotian campaign, which was intended to involve the full citizen levy as well as the professional marine and garrison troops, was decided on and acted out by the generals themselves, primarily Hippocrates and Demosthenes, as was the campaign against Megara.